Three-dimensional coordinates of individual atoms in materials revealed by electron tomography.

Crystallography, the primary method for determining the 3D atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal. Here, we report, for the first time, the determination of the 3D coordinates of thousands of individual atoms and a point defect in a material by electron tomography with a precision of ∼19 pm, where the crystallinity of the material is not assumed. From the coordinates of these individual atoms, we measure the atomic displacement field and the full strain tensor with a 3D resolution of ∼1 nm(3) and a precision of ∼10(-3), which are further verified by density functional theory calculations and molecular dynamics simulations. The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics, chemistry and biology.

[1]  Stephen J. Pennycook,et al.  Scanning transmission electron microscopy : imaging and analysis , 2011 .

[2]  Susanne Stemmer,et al.  Quantitative atomic resolution scanning transmission electron microscopy. , 2008, Physical review letters.

[3]  Zhifeng Huang,et al.  Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction. , 2013, Medical physics.

[4]  Michael K Miller,et al.  Invited review article: Atom probe tomography. , 2007, The Review of scientific instruments.

[5]  F. Hüe,et al.  Nanoscale holographic interferometry for strain measurements in electronic devices , 2008, Nature.

[6]  L. Liz‐Marzán,et al.  Atomic-scale determination of surface facets in gold nanorods. , 2012, Nature materials.

[7]  Alessandro Foi,et al.  Ieee Transactions on Image Processing a Closed-form Approximation of the Exact Unbiased Inverse of the Anscombe Variance-stabilizing Transformation , 2022 .

[8]  Bernd Kabius,et al.  Electron microscopy image enhanced , 1998, Nature.

[9]  Gabor T. Herman,et al.  Fundamentals of Computerized Tomography: Image Reconstruction from Projections , 2009, Advances in Pattern Recognition.

[10]  J. Miao,et al.  Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography. , 2008, Journal of structural biology.

[11]  Angus I Kirkland,et al.  Resolving strain in carbon nanotubes at the atomic level. , 2011, Nature materials.

[12]  Ulrich Dahmen,et al.  Operation of TEAM I in a User Environment at NCEM , 2012, Microscopy and Microanalysis.

[13]  G. Lu,et al.  Dissolution and diffusion properties of carbon in tungsten , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[14]  J. Miao,et al.  Equally sloped tomography with oversampling reconstruction , 2005 .

[15]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[16]  Stanley Osher,et al.  Development and Optimization of Regularized Tomographic Reconstruction Algorithms Utilizing Equally-Sloped Tomography , 2010, IEEE Transactions on Image Processing.

[17]  Garth J. Williams,et al.  Three-dimensional mapping of a deformation field inside a nanocrystal , 2006, Nature.

[18]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[19]  Gabor T. Herman,et al.  Image reconstruction from projections : the fundamentals of computerized tomography , 1980 .

[20]  D. Muller.  Structure and bonding at the atomic scale by scanning transmission electron microscopy. , 2009, Nature materials.

[21]  A. Minor,et al.  Observing and measuring strain in nanostructures and devices with transmission electron microscopy , 2014 .

[22]  A. Petford-Long,et al.  Atomic scale structure of sputtered metal multilayers , 2001 .

[23]  L D Marks,et al.  Wiener-filter enhancement of noisy HREM images. , 1996, Ultramicroscopy.

[24]  J. Miao,et al.  Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution , 2013, Nature.

[25]  J. Miao,et al.  Towards three-dimensional structural determination of amorphous materials at atomic resolution , 2013 .

[26]  R J Read,et al.  Crystallography & NMR system: A new software suite for macromolecular structure determination. , 1998, Acta crystallographica. Section D, Biological crystallography.

[27]  J. Miao,et al.  Electron tomography at 2.4-ångström resolution , 2012, Nature.

[28]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[29]  Earl J. Kirkland,et al.  Advanced Computing in Electron Microscopy , 1998 .

[30]  Haebum Lee,et al.  3D strain measurement in electronic devices using through-focal annular dark-field imaging. , 2014, Ultramicroscopy.

[31]  Ulrich Dahmen,et al.  Atomic-resolution imaging with a sub-50-pm electron probe. , 2009, Physical review letters.

[32]  O. L. Krivanek,et al.  Sub-ångstrom resolution using aberration corrected electron optics , 2002, Nature.

[33]  M. A. Oldfield,et al.  Fast Fourier method for the accurate rotation of sampled images , 1997 .

[34]  Emmanuel Brun,et al.  High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers , 2012, Proceedings of the National Academy of Sciences.

[35]  Carmelo Giacovazzo,et al.  Fundamentals of Crystallography , 2002 .

[36]  P. Midgley,et al.  3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography. , 2003, Ultramicroscopy.

[37]  J. Miao,et al.  Beyond crystallography: Diffractive imaging using coherent x-ray light sources , 2015, Science.

[38]  Greg L. Hura,et al.  Electron microscopy of gold nanoparticles at atomic resolution , 2014, Science.

[39]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[40]  Anthony J. G. Hey,et al.  Feynman And Computation , 2002 .